This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 2930 Spring 08 Prelim 1 1. Given the following differential equation dy dx = 4 x 2 y, y (0) = 0 (1) (a) Use Eulers method to approximate the differential equation on the interval x = [0 , 2]. Use a step size of h = 1 / 2 and clearly state any equations used. (b) Solve the differential equation dy dx = 4 x 2 y , y (0) = 0. (c) What is the error is Eulers method for y (2) in part (a)? 2. The population of a duck pond is governed by the following differential equation dP dt = 2 P (4 P ) , P (0) = 2 (2) (a) Solve for the population as a function of time, P ( t ). (b) What is the limiting population? 3. Find the general solution to the differential equation dy dx = x + 2 y y 2 x (3) For what initial conditions (if any) is the solution guaranteed to exist and be unique? 4. Given the differential equation below, answer the questions. dy dx = ( y 1)(2 y )( y r ) (4) (a) Calculate, then draw the bifurcation diagram for the system....
View
Full
Document
 Spring '07
 TERRELL,R
 Equations

Click to edit the document details